Preliminary Schedule of the Conference

Tuesday, May 2

10:00 - 10:30 Registration & Welcome coffee
10:30 - 10:45 Opening remarks
10:45 - 11:35 Bauer
11:45 - 12:35 Michael Kerber: Novel computational perspectives of Persistence
12:35 - 14:10 Lunch break
14:10 - 15:00 Giusti
15:10 - 16:00 Herlihy
16:00 - 16:30 Tea and cake
16:30 - 17:20 Rajsbaum
afterwards Reception

Wednesday, May 3

9:10 - 10:00 Chen
10:00 - 10:30 Group photo and coffee break
10:30 - 11:20 Yasu Hiraoka: Limit theorem for persistence diagrams and related topics
11:30 - 12:20 Reitzner
12:20 - 14:10 Lunch break
14:10 - 15:00 Brodzki
15:10 - 16:00 Weinberger
16:00 - 16:30 Tea and cake
16:30 - 17:30 Poster session

Thursday, May 4

9:10 - 10:00 Bianconi
10:00 - 10:30 Coffee break
10:30 - 11:20 Dmitri Krioukov: Exponential Random Simplicial Complexes
11:30 - 12:20 Meshulam
12:20 - Lunch break, free time (excursion?)

Friday, May 5

9:10 - 10:00 Fajstrup
10:00 - 10:30 Coffee break
10:30 - 11:20 Jérémy Dubut: Natural homology: computability and Eilenberg-Steenrod axioms
11:30 - 12:20 Krzysztof Ziemianski: Directed paths on cubical complexes
12:20 - 14:10 Lunch break
14:10 - 15:00 Peter Bubenik: Stabilizing the unstable output of persistent homology computations
15:10 - 16:00 Turner
16:00 - 16:30 Tea and cake
16:30 - 17:30 Software demonstrations and discussions

Saturday, May 6

9:10 - 10:00 Fasy
10:00 - 10:30 Coffee break
10:30 - 11:20 José Perea: Topological time series analysis and learning
11:30 - 12:20 Hubert Wagner: Topological Analysis in Information Spaces
12:20 Farewell

Abstracts

Peter Bubenik: Stabilizing the unstable output of persistent homology computations

Certain items of persistent homology computations are of particular interest to practitioners but are unfortunately unstable. For a notorious example, consider the generating cycle of a particular point in the persistence diagram. I will present a general framework for providing stable versions of such calculations. This is joint work with Paul Bendich and Alexander Wagner.

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Yasu Hiraoka: Limit theorem for persistence diagrams and related topics

In this talk, I will present a recent result about convergence of persistence diagrams on stationary point processes in RN. Several limit theorems such as strong laws of large numbers and central limit theorems for random cubical homology are also shown. If I have time, recent progress on higher dimensional generalization of Frieze zeta function theorem is also presented.

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Michael Kerber: Novel computational perspectives of Persistence

The computational pipeline of topological data analysis consists of three major steps:
(1) Deriving a multi-scale representation of the underlying data set
(2) Computing topological invariants of that representation
(3) Interpreting the outcome of (2) to draw conclusions about the data

In my talk, I will present new results in all three steps. In particular,
@(1) an approximation scheme for Rips and Cech complexes in high dimensions,
@(2) an algorithm to compute persistence diagrams of sequences of general simplicial maps,
@(3) an efficient implementation for computing Bottleneck and Wasserstein distances of peristence diagrams.

These results are joint work with Aruni Choudhary, Dmitriy Morozov, Arnur Nigmetov, Sharath Raghvendra and Hannah Schreiber.

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Hubert Wagner: Topological Analysis in Information Spaces

Understanding high dimensional data remains a challenging problem. Topological Data Analysis (TDA) promises to simplify, characterize and compare such data. However, standard TDA focuses on Euclidean spaces, while many types of high-dimensional data naturally live in non-Euclidean ones. Spaces derived from text, speech, image, … data are best characterized by non-metric dissimilarities, many of which are inspired by information-theoretical concepts. Such spaces will be called information spaces.

I will present the theoretical foundations of topological analysis in information spaces. First, intuition behind basic computational topology methods is given. Then, various dissimilarity measures are defined along with information theoretical and geometric interpretation. Finally, I will show how the framework of TDA can be extended to information spaces. In particular, I will explain to what extent existing software packages can be adapted to this new setting.

This is joint work with Herbert Edelsbrunner and Ziga Virk.

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